Royal pregnancy: Duchess of Cambridge 'feeling better'
The Duchess of Cambridge is "continuing to feel better" as she spends a third day in hospital with severe morning sickness, St James's Palace has said.
A spokesman said she and the Duke of Cambridge "are immensely grateful for the good wishes they have received".
Meanwhile, the Commonwealth realms have agreed to end discrimination against women succeeding to the British throne.
Deputy Prime Minister Nick Clegg said the legislation would be put before the Commons as soon as possible.
The Succession to the Crown Bill would mean the first child of the Duke and Duchess of Cambridge will become monarch, whether a boy or a girl. No due date has yet been announced for the baby.
The duchess is thought to be less than 12 weeks pregnant.
Catherine, whose pregnancy was announced on Monday, is being treated for acute morning sickness - or hyperemesis gravidarum - in the private King Edward VII Hospital in central London.
Her husband Prince William, who spent several hours visiting her on Monday, spent the day with her again on Tuesday.
The duchess was also visited by her main doctor Marcus Setchell and the royal gynaecologist Alan Farthing.
The new legislation will end the principle of male primogeniture, meaning male heirs will no longer take precedence over women in line to the throne.
It will also end the ban on anyone in the line of succession marrying a Roman Catholic.
The legislation was agreed in principle at the Commonwealth heads of government meeting in Perth, Australia in October 2011.
Since then, the government of New Zealand has been gathering formal letters of consent from the 15 realms of the Commonwealth, that have the Queen as their head of state.
They have confirmed they will be able to take the necessary measures in their own countries before the UK legislation comes into effect.
In a statement, Mr Clegg described the agreement as an "historic moment for our country and our monarchy".
He added: "People across the realms of the Commonwealth will be celebrating the news that the Duke and Duchess of Cambridge are expecting their first child.
"We can also all celebrate that whether the baby is a boy or a girl, they will have an equal claim to the throne."
The succession bill will require amendments to some of Britain's key constitutional documents, including the Bill of Rights and Coronation Oath Act of 1688, the 1701 Act of Settlement and the 1707 Act of Union between Scotland and England.